Question

100 POINTS

The product of a binomial and a trinomial is



`x^{4}\ +\ 7x^{3}\ -\ 2x^{2}\ +\ 3x^{2}\ +\ 6x\ -\ 5`



What would the equivalent expression be after it has been fully simplified?

Answer 1

Answer: So, the equivalent expression after simplification is `x^{4} + 7x^{3} + x^{2} + 6x - 5`.

Explanation:

To simplify the expression `x^{4} + 7x^{3} - 2x^{2} + 3x^{2} + 6x - 5`, we need to combine like terms by adding or subtracting the coefficients of the terms with the same exponent.

First, let's group the terms with the same exponent:

`x^{4} + 7x^{3} - 2x^{2} + 3x^{2} + 6x - 5`

Combining the terms with `x^4`, there is only one term: `x^{4}`.

Combining the terms with `x^3`, there is only one term: `7x^{3}`.

Combining the terms with `x^2`, we add `(-2x^{2})` and `(3x^{2})`, which gives us `x^{2}`.

Combining the terms with `x`, we add `6x` to get `6x`.

Finally, combining the constant terms `-5`, we have `-5`.

Putting it all together, the simplified expression is:

`x^{4} + 7x^{3} + x^{2} + 6x - 5`

So, the equivalent expression after simplification is `x^{4} + 7x^{3} + x^{2} + 6x - 5`.

If you have any more questions, feel free to ask.

Answer 2

`\sf x^4 + 7x^3 + x^2 + 6x - 5`

Explanation:

`\sf x^(4) + 7x^(3) - 2x^(2) + 3x^(2) + 6x - 5`

In order to simplify the given expression,we can combine like terms.

Start by grouping and adding the like terms together:

`\sf x^4 + 7x^3 - 2x^2 + 3x^2 + 6x - 5`

Combine the x² terms:

`\sf x^4 + 7x^3 + (3x^2 - 2x^2) + 6x - 5`

`\sf x^4 + 7x^3 + x^2 + 6x - 5`

Now, the expression is fully simplified, and we can write it as:

`\sf x^4 + 7x^3 + x^2 + 6x - 5`